What is the difference between 'prediction' and 'control' problem in the context of Reinforcement Learning?
Prediction is the problem of predicting any feature of the environment. In reinforcement learning, the typical feature is the reward or return, but this doesn't have to be always the case. See Multi-timescale nexting in a reinforcement learning robot (2011) by Joseph Modayil et al.
Control is the problem of estimating a policy. Clearly, the term control is related to control theory. In fact, the term control is often used as a synonym for action. See Is there any difference between a control and an action in reinforcement learning?. Similarly, the term controller is also used as a synonym for agent. For example, in the paper Metacontrol for Adaptive Imagination-Based Optimization (2017) by Jessica B. Hamrick et al. the term meta-controller is used to refer to an agent. A controlled system can also refer to the environment.
Section 14.1 of the book Reinforcement learning: an introduction (2nd edition) provides more details about the distinction between prediction and control and how this distinction is related to psychological concepts.